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Simplifying 91 = 2x2 + 3x + 1 Reorder the terms: 91 = 1 + 3x + 2x2 Solving 91 = 1 + 3x + 2x2 Solving for variable 'x'. Combine like terms: 91 + -1 = 90 90 + -3x + -2x2 = 1 + 3x + 2x2 + -1 + -3x + -2x2 Reorder the terms: 90 + -3x + -2x2 = 1 + -1 + 3x + -3x + 2x2 + -2x2 Combine like terms: 1 + -1 = 0 90 + -3x + -2x2 = 0 + 3x + -3x + 2x2 + -2x2 90 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2 Combine like terms: 3x + -3x = 0 90 + -3x + -2x2 = 0 + 2x2 + -2x2 90 + -3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 90 + -3x + -2x2 = 0 Factor a trinomial. (6 + -1x)(15 + 2x) = 0Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Subproblem 2
Set the factor '(15 + 2x)' equal to zero and attempt to solve: Simplifying 15 + 2x = 0 Solving 15 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + 2x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 2x = 0 + -15 2x = 0 + -15 Combine like terms: 0 + -15 = -15 2x = -15 Divide each side by '2'. x = -7.5 Simplifying x = -7.5Solution
x = {6, -7.5}
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